Details

Time bar (total: 9.6s)

analyze1.5s (16%)

Algorithm
search
Search
TrueOtherFalseIter
0%99.8%0.2%0
0%99.8%0.2%1
0%99.8%0.2%2
0%99.8%0.2%3
0%99.8%0.2%4
0%99.8%0.2%5
0%99.8%0.2%6
0%99.8%0.2%7
0%99.8%0.2%8
0%99.8%0.2%9
1.6%98.2%0.2%10
3.1%90.4%6.5%11
9.2%84.4%6.5%12
13%80.6%6.5%13
24.8%68.7%6.5%14
Compiler

Compiled 20 to 13 computations (35% saved)

sample1.7s (17.6%)

Symmetry

(sort x y)

(sort t a)

Results
1.2s8256×body128valid
417.0ms3187×body128invalid
Compiler

Compiled 59 to 38 computations (35.6% saved)

simplify58.0ms (0.6%)

Algorithm
egg-herbie
Rules
1034×fma-def_binary64
336×fma-neg_binary64
138×distribute-rgt-in_binary64
130×cancel-sign-sub-inv_binary64
128×associate-/r/_binary64
Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01321
12621
25221
38721
412821
516121
620321
724721
846421
982221
10123421
11116921
12123721
13131121
14137521
15137521
16128221

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022
Error
25.1b
Counts
2 → 1
Alt Table
StatusErrorProgram
25.1b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
Compiler

Compiled 57 to 36 computations (36.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.4b
(-.f64 (*.f64 z z) (*.f64 t a))
6.3b
(*.f64 (*.f64 x y) z)
9.2b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
24.4b
(sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))

series284.0ms (2.9%)

Counts
4 → 136
Calls

4 calls:

202.0ms
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
37.0ms
(sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))
37.0ms
(-.f64 (*.f64 z z) (*.f64 t a))
8.0ms
(*.f64 (*.f64 x y) z)

rewrite20.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
18×add-cbrt-cube_binary64
18×add-exp-log_binary64
11×add-sqr-sqrt_binary64
10×*-un-lft-identity_binary64
10×add-cube-cbrt_binary64
Counts
4 → 86
Calls

4 calls:

7.0ms
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))
4.0ms
(*.f64 (*.f64 x y) z)
3.0ms
(sqrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))
2.0ms
(-.f64 (*.f64 z z) (*.f64 t a))

simplify124.0ms (1.3%)

Algorithm
egg-herbie
Rules
731×fma-def_binary64
379×times-frac_binary64
318×associate-*r*_binary64
293×associate-*l*_binary64
277×associate-/l*_binary64
Counts
222 → 190
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02834463
18424196
238994138
349614138
449764138

prune148.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1819190
Fresh000
Picked101
Done000
Total1829191
Error
3.4b
Counts
191 → 9
Alt Table
StatusErrorProgram
23.1b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
24.5b
(*.f64 (/.f64 (*.f64 y x) (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))) (/.f64 z (sqrt.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
37.4b
(neg.f64 (*.f64 y x))
36.4b
(*.f64 y x)
45.7b
(*.f64 y (*.f64 (sqrt.f64 (/.f64 -1 (*.f64 a t))) (*.f64 z x)))
25.7b
(*.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (*.f64 a t)))))
25.4b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))))
38.7b
(/.f64 (*.f64 (*.f64 x y) z) z)
31.2b
(/.f64 1 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) (*.f64 y (*.f64 z x))))
Compiler

Compiled 5048 to 1533 computations (69.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
3.1b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
12.2b
(sqrt.f64 (neg.f64 (*.f64 a t)))

series715.0ms (7.4%)

Counts
3 → 52
Calls

3 calls:

485.0ms
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
212.0ms
(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
18.0ms
(sqrt.f64 (neg.f64 (*.f64 a t)))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
20×add-sqr-sqrt_binary64
19×*-un-lft-identity_binary64
19×add-cube-cbrt_binary64
18×times-frac_binary64
17×add-cbrt-cube_binary64
Counts
3 → 82
Calls

3 calls:

5.0ms
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
2.0ms
(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
1.0ms
(sqrt.f64 (neg.f64 (*.f64 a t)))

simplify82.0ms (0.8%)

Algorithm
egg-herbie
Rules
805×associate-/r*_binary64
302×associate-/r/_binary64
296×fma-def_binary64
227×cancel-sign-sub-inv_binary64
215×associate-*l*_binary64
Counts
134 → 137
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02393606
16023111
223073085
355263085

prune98.0ms (1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1352137
Fresh358
Picked011
Done000
Total1388146
Error
0.7b
Counts
146 → 8
Alt Table
StatusErrorProgram
31.2b
(/.f64 1 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) (*.f64 y (*.f64 z x))))
23.5b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
23.1b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
37.4b
(neg.f64 (*.f64 y x))
36.4b
(*.f64 y x)
25.7b
(*.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (*.f64 a t)))))
23.3b
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
25.4b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))))
Compiler

Compiled 3786 to 1181 computations (68.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

NewErrorProgram
0.1b
(/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))
1.1b
(*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
3.0b
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
12.2b
(sqrt.f64 (neg.f64 (*.f64 a t)))

series845.0ms (8.8%)

Counts
2 → 64
Calls

2 calls:

524.0ms
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
321.0ms
(*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))

rewrite16.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
16×add-sqr-sqrt_binary64
16×add-cbrt-cube_binary64
16×add-exp-log_binary64
14×associate-*r*_binary64
11×*-un-lft-identity_binary64
Counts
2 → 57
Calls

2 calls:

5.0ms
(*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z)))
5.0ms
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))

simplify80.0ms (0.8%)

Algorithm
egg-herbie
Rules
830×associate-/r*_binary64
362×associate-/r/_binary64
354×fma-def_binary64
261×cancel-sign-sub-inv_binary64
230×associate-*r*_binary64
Counts
121 → 114
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
02343901
16243028
223962984
357052984

prune128.0ms (1.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1851186
Fresh066
Picked011
Done101
Total1868194
Error
0.7b
Counts
194 → 8
Alt Table
StatusErrorProgram
24.1b
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z))))
23.3b
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z))))
31.2b
(/.f64 1 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) (*.f64 y (*.f64 z x))))
23.5b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
37.4b
(neg.f64 (*.f64 y x))
36.4b
(*.f64 y x)
25.7b
(*.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (*.f64 a t)))))
25.4b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))))
Compiler

Compiled 5095 to 1705 computations (66.5% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

NewErrorProgram
0.1b
(/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z))
0.2b
(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))
3.1b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))

series691.0ms (7.2%)

Counts
3 → 52
Calls

3 calls:

466.0ms
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
206.0ms
(/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z))
18.0ms
(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))

rewrite22.0ms (0.2%)

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt_binary64
26×associate-*r*_binary64
24×*-un-lft-identity_binary64
24×add-cube-cbrt_binary64
19×add-cbrt-cube_binary64
Counts
3 → 104
Calls

3 calls:

7.0ms
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
6.0ms
(*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t)))
2.0ms
(/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z))

simplify168.0ms (1.7%)

Algorithm
egg-herbie
Rules
591×fma-def_binary64
335×associate-*l*_binary64
305×associate-*r*_binary64
256×cancel-sign-sub-inv_binary64
241×fma-neg_binary64
Counts
156 → 205
Iterations

Useful iterations: 2 (0.0ms)

IterNodesCost
03004247
17983882
229593690
345593690
449773690
550003690
649363690

prune160.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New2032205
Fresh066
Picked011
Done101
Total2049213
Error
0.0b
Counts
213 → 9
Alt Table
StatusErrorProgram
42.0b
(*.f64 (/.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (neg.f64 t))) (sqrt.f64 (/.f64 1 a)))
23.5b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z)))
31.2b
(/.f64 1 (/.f64 (hypot.f64 (sqrt.f64 (neg.f64 (*.f64 a t))) z) (*.f64 y (*.f64 z x))))
23.6b
(*.f64 (*.f64 y x) (/.f64 z (hypot.f64 (*.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (sqrt.f64 (neg.f64 t)))) (sqrt.f64 (sqrt.f64 (neg.f64 t)))) z)))
37.4b
(neg.f64 (*.f64 y x))
36.4b
(*.f64 y x)
25.7b
(*.f64 (*.f64 y (*.f64 z x)) (sqrt.f64 (/.f64 1 (-.f64 (pow.f64 z 2) (*.f64 a t)))))
24.1b
(*.f64 y (*.f64 x (/.f64 z (hypot.f64 (*.f64 (sqrt.f64 a) (sqrt.f64 (neg.f64 t))) z))))
25.4b
(/.f64 (*.f64 (*.f64 x y) z) (sqrt.f64 (*.f64 (*.f64 (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a)))) (cbrt.f64 (-.f64 (*.f64 z z) (*.f64 t a))))))
Compiler

Compiled 5543 to 1688 computations (69.5% saved)

regimes2.3s (24.1%)

Accuracy

Total 4.2b remaining (66.6%)

Threshold costs 0b (0%)

Counts
96 → 5
Compiler

Compiled 19885 to 11537 computations (42% saved)

bsearch194.0ms (2%)

Steps
ItersRangePoint
8
1.2931480003165196e+27
1.9589842908440882e+31
1.216315346182611e+31
8
1.251225119420865e-139
5.743366612777225e-137
3.916159283675478e-139
6
-5.764931901109984e-203
-8.444854958642352e-204
-5.653067374710907e-203
6
-3.5348758200678786e+155
-4.9301349217216476e+154
-4.988987613997654e+154
Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0.1%)

Algorithm
egg-herbie
Rules
14×*-commutative_binary64
+-commutative_binary64
sub-neg_binary64
neg-sub0_binary64
neg-mul-1_binary64
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
048111
173111
290111
3100111
4104111
5102111

end176.0ms (1.8%)

Remove

(sort t a)

(sort x y)

Compiler

Compiled 646 to 364 computations (43.7% saved)

Profiling

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